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Properties

Label 608.2
Level 608
Weight 2
Dimension 6274
Nonzero newspaces 18
Newform subspaces 41
Sturm bound 46080
Trace bound 9

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Defining parameters

Level: \( N \) = \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 41 \)
Sturm bound: \(46080\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(608))\).

Total New Old
Modular forms 12096 6614 5482
Cusp forms 10945 6274 4671
Eisenstein series 1151 340 811

Trace form

\( 6274 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 60 q^{5} - 64 q^{6} - 46 q^{7} - 64 q^{8} - 94 q^{9} + O(q^{10}) \) \( 6274 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 60 q^{5} - 64 q^{6} - 46 q^{7} - 64 q^{8} - 94 q^{9} - 80 q^{10} - 46 q^{11} - 96 q^{12} - 76 q^{13} - 96 q^{14} - 54 q^{15} - 104 q^{16} - 40 q^{17} - 104 q^{18} - 50 q^{19} - 168 q^{20} - 64 q^{21} - 88 q^{22} - 62 q^{23} - 40 q^{24} - 98 q^{25} - 24 q^{26} - 94 q^{27} - 24 q^{28} - 44 q^{29} - 86 q^{31} - 24 q^{32} - 164 q^{33} - 40 q^{34} - 94 q^{35} - 8 q^{36} - 60 q^{37} - 76 q^{38} - 148 q^{39} - 88 q^{40} - 120 q^{41} - 104 q^{42} - 62 q^{43} - 144 q^{44} - 100 q^{45} - 128 q^{46} - 54 q^{47} - 168 q^{48} - 22 q^{49} - 144 q^{50} - 38 q^{51} - 80 q^{52} - 124 q^{53} - 88 q^{54} + 18 q^{55} - 88 q^{56} - 104 q^{57} - 128 q^{58} + 18 q^{59} - 56 q^{60} - 108 q^{61} - 24 q^{62} + 42 q^{63} + 8 q^{64} - 140 q^{65} - 16 q^{66} + 34 q^{67} - 104 q^{68} - 128 q^{69} - 40 q^{70} + 18 q^{71} - 112 q^{72} - 88 q^{73} - 96 q^{74} - 40 q^{75} - 68 q^{76} - 168 q^{77} - 144 q^{78} - 54 q^{79} - 56 q^{80} - 54 q^{81} - 64 q^{82} - 126 q^{83} - 104 q^{84} - 96 q^{85} - 24 q^{86} - 158 q^{87} - 72 q^{88} - 120 q^{89} - 88 q^{90} - 142 q^{91} + 8 q^{92} - 40 q^{93} - 88 q^{94} - 110 q^{95} - 144 q^{96} - 200 q^{97} - 24 q^{98} - 150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
608.2.a \(\chi_{608}(1, \cdot)\) 608.2.a.a 1 1
608.2.a.b 1
608.2.a.c 1
608.2.a.d 1
608.2.a.e 1
608.2.a.f 1
608.2.a.g 2
608.2.a.h 2
608.2.a.i 4
608.2.a.j 4
608.2.b \(\chi_{608}(303, \cdot)\) 608.2.b.a 2 1
608.2.b.b 4
608.2.b.c 12
608.2.c \(\chi_{608}(305, \cdot)\) 608.2.c.a 2 1
608.2.c.b 16
608.2.h \(\chi_{608}(607, \cdot)\) 608.2.h.a 20 1
608.2.i \(\chi_{608}(353, \cdot)\) 608.2.i.a 2 2
608.2.i.b 2
608.2.i.c 8
608.2.i.d 8
608.2.i.e 8
608.2.i.f 12
608.2.k \(\chi_{608}(153, \cdot)\) None 0 2
608.2.m \(\chi_{608}(151, \cdot)\) None 0 2
608.2.n \(\chi_{608}(31, \cdot)\) 608.2.n.a 40 2
608.2.s \(\chi_{608}(335, \cdot)\) 608.2.s.a 4 2
608.2.s.b 4
608.2.s.c 28
608.2.t \(\chi_{608}(49, \cdot)\) 608.2.t.a 36 2
608.2.u \(\chi_{608}(75, \cdot)\) 608.2.u.a 312 4
608.2.v \(\chi_{608}(77, \cdot)\) 608.2.v.a 288 4
608.2.y \(\chi_{608}(161, \cdot)\) 608.2.y.a 24 6
608.2.y.b 30
608.2.y.c 30
608.2.y.d 36
608.2.z \(\chi_{608}(121, \cdot)\) None 0 4
608.2.bb \(\chi_{608}(103, \cdot)\) None 0 4
608.2.bf \(\chi_{608}(17, \cdot)\) 608.2.bf.a 108 6
608.2.bh \(\chi_{608}(15, \cdot)\) 608.2.bh.a 12 6
608.2.bh.b 96
608.2.bi \(\chi_{608}(127, \cdot)\) 608.2.bi.a 120 6
608.2.bm \(\chi_{608}(45, \cdot)\) 608.2.bm.a 624 8
608.2.bn \(\chi_{608}(27, \cdot)\) 608.2.bn.a 624 8
608.2.bo \(\chi_{608}(71, \cdot)\) None 0 12
608.2.bq \(\chi_{608}(9, \cdot)\) None 0 12
608.2.bs \(\chi_{608}(5, \cdot)\) 608.2.bs.a 1872 24
608.2.bt \(\chi_{608}(3, \cdot)\) 608.2.bt.a 1872 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(608))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(608)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)